If the distance between the foci

We know that equation of Hyperbola

$=\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$

Also we have foci $=(\pm a e, 0)$

Given distance between foci is $2 \mathrm{ae}=16$

$e=\sqrt{2}$

$2 \times a \times \sqrt{2}=16$

$a=\frac{16}{2 \times \sqrt{2}}=\frac{8}{\sqrt{2}}=4 \sqrt{2}$

$\because b^{2}=a^{2}\left(e^{2}-1\right)$

$\mathrm{b}^{2}=(4 \sqrt{2})^{2}\left((\sqrt{2})^{2}-1\right)$

$=32(2-1)=32$

$\therefore$ Equation is $\frac{x^{2}}{32}-\frac{y^{2}}{32}=1$